Electromotive force

In physics, electromotive force, or most commonly emf , or (occasionally) electromotance is "that which tends to cause current (actual electrons and ions) to flow."

More formally, emf is the external work expended per unit of charge to produce an electric potential difference across two open-circuited terminals. The electric potential difference is created by separating positive and negative charges, thereby generating an electric field. The created electrical potential difference drives current flow if a circuit is attached to the source of emf. When current flows, however, the voltage across the terminals of the source of emf is no longer the open-circuit value, due to voltage drops inside the device due to its internal resistance.

Devices that can provide emf include voltaic cells, thermoelectric devices, solar cells, electrical generators, transformers, and even Van de Graaff generators.

In the case of a battery, charge separation that gives rise to a voltage difference is accomplished by chemical reactions at the electrodes; a voltaic cell can be thought of as having a "charge pump" of atomic dimensions at each electrode, that is:

"A source of emf can be thought of as a kind of charge pump that acts to move positive charge from a point of low potential through its interior to a point of high potential. … By chemical, mechanical or other means, the source of emf performs work dW on that charge to move it to the high potential terminal. The emf ℰ of the source is defined as the work dW done per charge dq: ℰ = dW/dq."

The reactions at the electrode–electrolyte interfaces provide the "seat" of emf for the voltaic cell, that is, these reactions drive the current.In the open-circuit case, charge separation continues until the electrical field from the separated charges is sufficient to arrest the reactions.

In the case of an electrical generator, a time-varying magnetic field inside the generator creates an electric field via electromagnetic induction, which in turn creates an energy difference between generator terminals. Charge separation takes place within the generator, with electrons flowing away from one terminal and toward the other, until, in the open-circuit case, sufficient electric field builds up to make further movement unfavorable. Again the emf is countered by the electrical voltage due to charge separation. If a load is attached, this voltage can drive a current. The general principle governing the emf in such electrical machines is Faraday's law of induction.

A solar cell or photodiode is another source of emf, with light energy as the external power source.


Formal definitions of electromotive force

Inside a source of emf that is open-circuited, the conservative electrostatic field created by separation of charge exactly cancels the forces producing the emf. Thus, the emf has the same value but opposite sign as the integral of the electric field aligned with an internal path between two terminals A and B of a source of emf in open-circuit condition (the path is taken from the negative terminal to the positive terminal to yield a positive emf, indicating work done on the electrons moving in the circuit). Mathematically:

where E_cs is the conservative electrostatic field created by the charge separation associated with the emf, dℓ is an element of the path from terminal A to terminal B, and ‘·’ denotes the vector dot product . This equation applies only to locations A and B that are terminals, and does not apply to paths between points A and B with portions outside the source of emf. This equation involves the electrostatic electric field due to charge separation E_cs and does not involve (for example) any non-conservative component of electric field due to Faraday's law of induction.

In the case of a closed path in the presence of a varying magnetic field , the integral of the electric field around a closed loop may be nonzero; one common application of the concept of emf, known as "induced emf" is the voltage induced in a such a loop. The "induced emf" around a stationary closed path C is:

where now E is the entire electric field, conservative and non-conservative, and the integral is around an arbitrary but stationary closed curve C through which there is a varying magnetic field. Note that the electrostatic field does not contribute to the net emf around a circuit because the electrostatic portion of the electric field is conservative (that is, the work done against the field around a closed path is zero).

This definition can be extended to arbitrary sources of emf and moving paths C:

which is a conceptual equation mainly, because the determination of the "effective forces" is difficult.